How do I properly normalize a function over a region in space?

[germana2006]

Homework Statement

I have normalized the following function:

$$Q=\int (1-y^2) dx dy$$

Homework Equations

using the expression for the normalization

$$\vert N \vert ^2 \vert \int Q^* Q dx dy \vert^2 =1$$

The Attempt at a Solution

then I obtained

$$\int Q^* Q dx dy = x (y- y^3 /3)$$

therefore

$$N = 1/ x (y- y^3 /3)$$

but I am not sure if I have done good.

 

[DavidWhitbeck]

You normalize functions over regions in space. The normalization factor should not be a function of anything but perhaps the boundary of the region you're examining.

And you either stated your function Q incorrectly or you evaluated the double integral incorrectly. Also you stated your normalization equation wrong, you're doubling up on the squaring.

You need to start over from the beginning.